Abstract
This paper outlines a logic programming methodology which applies standardized logic program recursion forms afforded by a system of general purpose recursion schemes. The recursion schemes are conceived of as quasi higher-order predicates which accept predicate arguments, thereby representing parameterized program modules. This use of higher-order predicates is analogous to higher-order functionals in functional programming. However, these quasi higher-order predicates are handled by a metalogic programming technique within ordinary logic programming.
Some of the proposed recursion operators are actualizations of mathematical induction principles (e.g. structural induction as generalization of primitive recursion). Others are heuristic schemes for commonly occurring recursive program forms. The intention is to handle all recursions in logic programs through the given repertoire of higher-order predicates.
We carry out a pragmatic feasibility study of the proposed recursion operators with respect to the corpus of common textbook logic programs.
This pragmatic investigation is accompanied with an analysis of the theoretical expressivity. The main theoretical results concerning computability are
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(1)
Primitive recursive functions can be re-expressed in logic programming by predicates defined solely by non-recursive clauses augmented with afold recursion predicate akin to the fold operators in functional programming.
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(2)
General recursive functions can be re-expressed likewise sincefold allows re-expression of alinrec recursion predicate facilitating linear, unbounded recursion.
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Andreas Hamfelt, Ph.D.: He currently works as an associate professor at the Computing Science Department, Uppsala University. His interests are in structured programming methodology for relational programming, inductive logic programming, program synthesis, metalogic programming, and knowledge representation of administrative decision making. He obtained an M.Sc. in Computing Science in 1987 from Uppsala University, where he also received his Ph.D. in 1992.
Jørgen Fischer Nilsson, Ph.D.: He is a professor at Department of Information Technology at the Technical University of Denmark (DTU). He received his Ph.D. in computer science from DTU in 1977. In 1976–77 he was visiting researcher at computer science department at IBM Research Laboratories, San José, California. Since 1980 he has been at DTU where he became professor in knowledge based systems 1988. His main research fields are knowledge representation, knowledge based systems, and logic programming methodology and applications.
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Hamfelt, A., Nilsson, J.F. Towards a logic programming methodology based on higher-order predicates. NGCO 15, 421–447 (1997). https://doi.org/10.1007/BF03037300
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DOI: https://doi.org/10.1007/BF03037300